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It happens in the time between birth by sleep and Kingdom Hearts, when Xehanort is apprentice to Ansem the Wise. Throughout the series, it is implied and accepted that his heart succumbed to darkness. No details of this occurrence are even shown in cutscenes.

That is, until Kingdom Hearts 3D. In the opening scene, Apprentice Xehanort is shown extracting Braig's heart manually via Master Xehanort's keyblade, so this may imply that he did this to himself as well.